Intersecting brane solutions in string and M-theory

Abstract

We review various aspects of configurations of intersecting branes, including the conditions for preservation of supersymmetry. In particular, we discuss the projection conditions on the Killing spinors for given brane configurations and the relation to calibrations. This highlights the close connection between intersecting branes and branes wrapping supersymmetric cycles as well as special holonomy manifolds. We also explain how these conditions can be used to find supergravity solutions without directly solving the Einstein equations. The description of intersecting branes is considered both in terms of the brane worldvolume theories and as supergravity solutions. There are well-known simple procedures (harmonic function rules) for writing down the supergravity solutions for supersymmetric configurations of orthogonally intersecting branes. However, such solutions involve smeared or delocalised branes. We describe several methods of constructing solutions with less smearing, including some fully localised solutions. Some applications of these supergravity solutions are also considered -in particular the study of black holes and gauge theories.

Brane webs and 1/4-BPS geometries

“…By adding a brane to R 9,1 one breaks half of the supersymmetries and the appropriate projections are [25] (see also [26] for a review):…”

“…(6.65) 26 Notice that the Monge-Ampere equation appearing in (6.2) can be rewritten in terms of a new variable y 2 , an absence of branch cuts in this new description implies that K has expansions in integer powers of…”

Holographic cosmology from a system of M2–M5 branes

“…This analysis has been done using the blackfold approach. Thus, it has been possible to recover the 1/4-BPS self-dual string solution [30]- [31], as a three-funnel solution of an effective five-brane world volume theory [32]- [35]. The finite temperature effects for non-extremal self-dual string solution solutions and wormhole solutions interpolating between stacks of M5-branes and anti-M5-branes have also been studied.…”

Supergravity solutions of two M2 branes

“…As long as the near core region of supersymmetic BPS solutions of brane sysytems is of importance in bulk-boundary duality, numerous solutions of orthogonal intersecting M branes have been constructed [1]- [9], [15]- [17].…”